Simplify the following expression: $ z = \dfrac{10}{-7x + 2} - \dfrac{-6}{5} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{10}{-7x + 2} \times \dfrac{5}{5} = \dfrac{50}{-35x + 10} $ Multiply the second expression by $\dfrac{-7x + 2}{-7x + 2}$ $ \dfrac{-6}{5} \times \dfrac{-7x + 2}{-7x + 2} = \dfrac{42x - 12}{-35x + 10} $ Therefore $ z = \dfrac{50}{-35x + 10} - \dfrac{42x - 12}{-35x + 10} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{50 - (42x - 12) }{-35x + 10} $ Distribute the negative sign: $z = \dfrac{50 - 42x + 12}{-35x + 10}$ $z = \dfrac{-42x + 62}{-35x + 10}$ Simplify the expression by dividing the numerator and denominator by -1: $z = \dfrac{42x - 62}{35x - 10}$